Large bounded degree trees in expanding graphs.
Large deviations in randomly coloured random graphs.
Large holes in quasi-random graphs.
Large trees in random graphs
Limit distributions and random trees derived from the birthday problem with unequal probabilities.
Limit theorems for the weights and the degrees in anN-interactions random graph model
A random graph evolution based on interactions of N vertices is studied. During the evolution both the preferential attachment rule and the uniform choice of vertices are allowed. The weight of an M-clique means the number of its interactions. The asymptotic behaviour of the weight of a fixed M-clique is studied. Asymptotic theorems for the weight and the degree of a fixed vertex are also presented. Moreover, the limits of the maximal weight and the maximal degree are described. The proofs are based...
Local extrema in random trees.
Logarithmic components of the vacant set for random walk on a discrete torus.
Logconcave random graphs.
Loose Hamilton cycles in random 3-uniform hypergraphs.
Loose Hamilton cycles in random uniform hypergraphs.
Lower bounds for the size of random maximal -free graphs.